Give examples of linear equations in one variable with one solution (𝑥 = 𝑎), infinitely many solutions (𝑎 = 𝑎), or no solutions (𝑎 = 𝑏). Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form 𝑥 = 𝑎, 𝑎 = 𝑎,𝑜𝑟 𝑎 = 𝑏 results (where 𝑎 and 𝑏 are different numbers).
Expressions and Equations
- Analyze and solve linear equations and inequalities.
Fluently (efficiently, accurately, and flexibly) solve one-step, two-step, and multi-step linear equations and inequalities in one variable, including situations with the same variable appearing on both sides of the equal sign.